# Category Archive for: Symbolic Processing with MATLAB

Positioning a Robot Ann Figure 10.2-2 shows a robot arm having two joints and two links. The angles of rotation of the motors at the joints are 8. and (h. From tri gonornetry we can derive the following expressions for the (x, y) coordinates of the hand: x = L, cos 9, + L2 cos(9, +…

Topping the Green Monster The Green Monster is a wall 37 ft high in left field at Fenway Park in Boston. The wall 310 ft from home plate down the left-field line, Assuming that the batter hits the ball above the ground, and neglecting air resistance, determine the minimum speed the must give to the ball to hit…

Differential Equations A first-order ordinary differential equation (ODE) can be written in the form dy dt = f(t, y) where t is the independent variable and y is a function of t. A solution to such an equation is a function y = g(t) such that dgf dt = f(t, g), and the solution will contain one arbitrary constant.…

Laplace Transforms This section explains how to use the Laplace transform with MATLAB to solve some types of differential equations that cannot be solved with dsol ve. Application of the Laplace transform converts a linear differential equation problem into an algebraic problem. With proper algebraic manipulation of the resulting quantities, the solution of the differential equation can be recovered…

Algebraic and Transcendental Equations The Symbolic Math toolbox can solve algebraic and transcendental equations, well as systems of such equations. A transcendentaL equation is one that contain one or more transcendental functions, such as sin x, e”, or log x. The appropriate function to solve such equations is the sol ve function. The function solve (E) solves a symbolic…

Symbolic Expressions and Algebra The sym function can be used to create “symbolic objects” in MATLAB. If the  input argument to sym is a string, the result is a symbolic number or variable. If the input argument is a numeric scalar or matrix, the result is a symbolic representation of the given numeric values. For example, typing…

Problems You can find the answers to problems marked with an asterisk at the end of the text. Section 10.1 . Use MATLAB to prove the following identities: a. sin2 x +cos2 X = 1 b. sin(x + y) = sin r cosy +cosx sin y c. sin 2x = 2 sinx cosx d. COSh2X ~…

Intersection of Two Circles We want to find the intersection points of two circles. The first circle has a radius of 2 and is centered at x= 3, y = 5. The second circle has a radius b and is centered at x = 5, y = 3. See Figure 10.2-1. (a) Find the (x, y)…

Symbolic Linear Algebra You can perform operations with symbolic matrices in much the same way as .with numeric matrices. Here we give examples of finding matrix products, the matrix inverse, eigenvalues, and the characteristic polynomial of a matrix  Remember that using symbolic matrices avoids numerical imprecision in subsequent operations. You can create a symbolic matrix from a numeric…

Calculus In Chapter 8 we discussed techniques for performing numerical differentiation and numerical integration; this section covers differentiation and integration of symbolic expressions to obtain closed form results for the derivatives and integrals. Differentiation The di f f function is used to obtain the symbolic derivative. Although this function has the same name as the function used to…